# HW_2 - ISyE 3133 C Engineering Optimization Homework Assignment 2 Issued Due Date September 4 2009 1[15 points Answer the following questions a

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ISyE 3133 C - Engineering Optimization Homework Assignment # 2 Issued: August 26, 2009 Due Date: September 4, 2009 1. [15 points] Answer the following questions: a) What are the definitions of linear independence, subspace, linear span of a set of vectors, and basis of a subspace? b) Consider the vectors v 1 , . .., v k Ը n . Recall that v 1 Ը n means that the vector v 1 has n elements, each of which is a real number. Suppose v 1 , . .., v k are linearly independent. - Can k > n? Why? - Is Ը n a subspace? Why? - What would k have to equal for v 1 , . .., v k to be a basis for Ը n ? c) Suppose A Ը 3 x 4 . Recall that this means that A is a matrix with 3 rows and 4 columns and all its entries are real numbers. - What is the maximum possible number of linearly independent columns of A ? - What is the definition of rank( A ) ? - What can you say about rank( A ) from the fact that A Ը 3 x 4 ? d) Given a nonsingular square matrix B . - What is the definition of its inverse B 1 ? - What can you say about det( B ) - the determinant of B ? e) Given a matrix B Ը mxm with inverse B 1 , a vector b Ը m , and the system of equations B x = b, solve for x Ը

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## This note was uploaded on 09/07/2009 for the course COE 2001 taught by Professor Valle during the Fall '08 term at Georgia Institute of Technology.

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HW_2 - ISyE 3133 C Engineering Optimization Homework Assignment 2 Issued Due Date September 4 2009 1[15 points Answer the following questions a

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